Book A Free Math Class # 2D Shapes - Names, Properties, and Examples [#Geometry](/content/tag/geometry/index.html) TL;DR 2D shapes are flat figures with only two dimensions, length and width, and no thickness. This article names the common 2D shapes (circle, triangle, square, rectangle, pentagon, hexagon, octagon), explains their sides, vertices, and angles, shows how to find area and perimeter, and clears up the mistakes students make most BT [Bhanzu Team](/content/authors/bhanzu-team/index.html) Last updated on July 21, 2026 9 min read ## What Are 2D Shapes? A **2D shape** (two-dimensional shape) is a **flat figure** that has only two dimensions - **length and width** and no thickness or depth. You can draw a 2D shape on a sheet of paper; you cannot pick one up, because it has no third dimension to hold. Contrast this with a **3D shape** like a cube or a ball, which adds depth and takes up space. A drawing of a square is 2D; a dice is 3D. The flat face of that dice, though, is a 2D square - every 3D solid is built from 2D faces. Most 2D shapes are described by three features: - **Sides** - the straight (or curved) lines that form the boundary. - **Vertices** - the corners, the points where two sides meet. A shape has as many vertices as it has sides. - **Angles** - the openings formed where two sides meet at a vertex. A circle is the odd one out: it has one continuous curved boundary, no straight sides, and no vertices. Shapes made only of straight sides are called [polygons](/content/math/terms/polygon/index.html); a circle is not a polygon. ## What Are the Names of the Common 2D Shapes? The everyday 2D shapes, grouped by how many sides they have. Here we introduce each shape before using its properties. | Shape | Sides | Vertices | Key property | |-----------|---------------|----------|------------------------------------------------------------| | Circle | 0 straight | 0 | One curved boundary; every boundary point is equidistant from the centre | | Triangle | 3 | 3 | Interior angles sum to 180° | | Square | 4 | 4 | Four equal sides, four 90° angles | | Rectangle | 4 | 4 | Opposite sides equal, four 90° angles | | Rhombus | 4 | 4 | Four equal sides, opposite angles equal | | Pentagon | 5 | 5 | Interior angles sum to 540° | | Hexagon | 6 | 6 | Interior angles sum to 720° | | Octagon | 8 | 8 | Interior angles sum to 1080° | A few shapes deserve a closer look: - A [**triangle**](/content/math/geometry/types-of-triangle/index.html) is the simplest polygon - three sides, three angles that always add to 180°. - A **square** is a special rectangle where all four sides are equal. It is also a special rhombus. (Yes, [a square is a rectangle](/content/math/geometry/is-a-square-a-rectangle/index.html).) - A [**hexagon**](/content/math/geometry/hexagon/index.html) shows up in honeycombs because hexagons tile a flat surface with no gaps and minimal material. ## Regular vs Irregular 2D Shapes A shape is **regular** when all its sides are equal _and_ all its angles are equal - like a square or an equilateral triangle. A shape is [**irregular**](/content/math/geometry/irregular-polygons/index.html) when its sides or angles are not all equal - like a scalene triangle or a rectangle that isn't a square. **Is a rectangle regular?** No - its angles are all 90°, but its sides are not all equal, so it fails the "all sides equal" half of the test. A regular four-sided shape must be a square. ## How Do You Find the Area and Perimeter of 2D Shapes? **Perimeter** is the total distance around the boundary - add up all the side lengths. **Area** is the amount of flat space the shape covers, measured in square units. Common formulas, with what each symbol means: | Shape | Area | Perimeter | |-----------|--------------------------|---------------------| | Square | s² (s = side) | 4s | | Rectangle | lw (l = length, w = width) | 2(l + w) | | Triangle | (1/2)bh (b = base, h = height) | sum of the three sides | | Circle | πr² (r = radius) | 2πr (called circumference) | The square's area is s² because you tile it with rows and columns of unit squares: s across, s down, so s² small squares fit inside. Every area formula has a picture behind it - it is never just a rule to memorise. ## Examples of 2D Shapes Six worked examples, easier to harder. The problem statement is bold; the steps are not. We use ⋅ for every product. ### Example 1 **A square has a side of 6 cm. Find its perimeter and area.** Perimeter = 4⋅6 = 24 cm. Area = 6² = 36 cm². Final answer: perimeter 24 cm, area 36 cm². ### Example 2 **A rectangle is 8 cm long and 5 cm wide. A student says its area is 8 + 5 = 13. Is that right?** The tempting move is to add the two dimensions, because that is what you do for perimeter-like thinking. Adding gives 13. But area counts the _squares that fit inside_, which means you multiply: Area = l⋅w = 8⋅5 = 40 cm². The real answer is 40 cm², not 13. Adding the sides gives you (half) the perimeter, not the area. Area is always length **times** width for a rectangle. ### Example 3 **A triangle has a base of 10 cm and a height of 6 cm. Find its area.** Area = (1/2)⋅b⋅h = (1/2)⋅10⋅6 = 30 cm² Final answer: 30 cm². ### Example 4 **A circle has a radius of 7 cm. Find its area. Use π ≈ 22/7.** Area = πr² = (22/7)⋅7² = (22/7)⋅49 = 154 cm². Final answer: 154 cm². ### Example 5 **A regular hexagon has each side measuring 4 cm. Find its perimeter, and state the sum of its interior angles.** Perimeter = 6⋅4 = 24 cm. Sum of interior angles of any polygon is (n−2)⋅180°, where n is the number of sides. For a hexagon n=6: (6−2)⋅180° = 720°. Final answer: perimeter 24 cm; interior angles sum to 720°. ### Example 6 **A rectangular garden is 12 m by 9 m. A circular pond of radius 3 m sits inside it. What area of the garden is left as lawn? Use π ≈ 3.14.** Garden area = 12⋅9 = 108 m². Pond area = πr² = 3.14⋅3² = 28.26 m². Lawn = 108−28.26 = 79.74 m². Final answer: about 79.74 m² of lawn. Real problems often combine two shapes - find each area, then subtract. ## Why 2D Shapes Matter 2D shapes are the layer where geometry becomes useful, because almost everything we design starts as a flat plan. The real reason they earn a whole chapter: - **Every 3D object is built from 2D faces.** A cube is six squares; a box is six rectangles; a can's label unrolls into a rectangle. - **Plans, maps, and screens are 2D.** An architect's blueprint, a city map, a phone screen - all reduce a 3D world to flat shapes so we can measure and reason about them. - **Tiling and packing.** Only certain regular shapes tile a plane with no gaps - triangles, squares, and hexagons. That is why floor tiles and [honeycombs](https://en.wikipedia.org/wiki/Honeycomb_conjecture) look the way they do. The historical thread runs through [Euclid](https://mathshistory.st-andrews.ac.uk/Biographies/Euclid/), whose _Elements_ (about 300 BCE) built all of plane geometry from a handful of assumptions about points, lines, and flat figures. ## The Mistakes Students Make Most Often Three mix-ups cause most trouble with 2D shapes. ### Mistake 1: Confusing area with perimeter **Where it slips in:** any problem that gives length and width and asks for "how much" (the rusher who grabs the first operation that comes to mind). **Don't do this:** add the sides when the question asks for area. **The correct way:** perimeter is the _distance around_ (add the sides); area is the _space inside_ (multiply, in square units). ### Mistake 2: Assuming every four-sided shape is a square **Where it slips in:** naming shapes quickly. **Don't do this:** call a rectangle or a rhombus a square. ### Mistake 3: Treating a circle as a polygon **Where it slips in:** listing "sides" and "vertices". **Don't do this:** say a circle has one side, or count a vertex where there is only a smooth curve. ## Conclusion - **2D shapes** are flat figures with length and width but no thickness. - They are described by their sides, vertices, and angles; a circle has a curved boundary and no vertices. - Regular shapes have all sides _and_ all angles equal; irregular ones do not. - Perimeter adds the sides; area multiplies to measure the space inside, in square units. - Every 3D solid is built from 2D faces, which is why these shapes are the foundation of geometry.